A two terminal black box contains one of the R.L.C. elements.

A two terminal black box contains one of the R.L.C. elements. The black box is connected to a 220 volts A.C. supply. The current through the source is I. When a capacitance of 0.1F is inserted in the series between the source and the box, the current through the source is 2I. The element is

1. a resistance
2. an inductance
3. a capacitance of 0.5F
4. it is not possible to determine the element.

Initially , I =	V
	R + jX

When capacitance inserted,

2I =	V
	R + jX - jωC

⇒	2	+	6
	R + jX		R + jX - (j / ωC)

⇒ 2R + 2jX -	2j	= R + jX
	ωC

⇒ R + jX =	2j
	ωC

X =	2
	ωC

Here ‘+’ ve sign element is inductance